The approaches described in this section could be pursued, but are not necessarily approaches that have previously been conceived or pursued. Therefore, unless otherwise indicated, it should not be assumed that any of the approaches described in this section qualify as prior art merely by virtue of their inclusion in this section.
Electrical impedance, electrical capacitance, and microwave tomography have the potential to become powerful tools in the fields of medicine, security, and manufacturing and other fields that would benefit from the wealth of diagnostic information that can be gleaned from materials' dielectric properties. Unlike X-ray or ultrasound measurements that primarily indicate materials' density, dielectric properties can be unique to individual materials and can be used to, for example, identify specific tissues or tumors, or distinguish between explosives and foodstuffs. To date, these dielectric imaging techniques have found limited use in boutique diagnostics or in specific situations that permit dielectric measurements to be made.
Materials' dielectric properties are not readily resolved to specific spatial regions because dielectric structures can bend, contort, reflect, and diffract the propagation of electromagnetic fields in non-linear ways, which obscures both their spatial position and underlying dielectric characteristics.
The path of an electromagnetic field through a subject (i.e. specimen) under study will vary according to the frequency or, more generally, the rate of change of the field. In static conditions, or where wavelengths are an order of magnitude or more longer than the dielectric structures under investigation, the impedance characteristics of the subject under study will determine the paths of the current—fields will be drawn into the material of lowest impedance. As the frequency increases, however, propagation will take on more ray-like behaviors, and propagation will be dominated by the material of highest propagation velocity.
Traditionally, these two regimes are approached differently. Low-frequency or static techniques like electrical impedance tomography (EIT) or electrical capacitance tomography (ECT)—often called soft-field tomography because the bending and curving of the fields contrasts with the hard-field or straight line of X-rays through an object—apply an array of electrodes to the surface of an object under study and sequentially apply currents through pairs of electrodes to map out equipotential lines. A computer algorithm then iterates through the possible impedances of regions to match the equipotential curves measured in the data.
Low-frequency or static EIT/ECT fields can greatly obscure internal detail, especially at appreciable distance from a dielectric structure, because the fields tend to smooth out with distance. Static techniques also struggle with multi-layer structures—a key reason why EIT/ECT electrodes are directly applied to an object under study because an air gap would add a high impedance layer and impedance boundaries can obscure field structures within.
At much higher frequencies, techniques such as microwave tomography (MWT) use wavelengths similar to the size of the dielectric structures under study. At these frequencies, waves freely propagate and take on more ray-like characteristics. Although microwave paths can be more linear through some structures, they typically do not deeply penetrate subjects (i.e. specimens) of interest—such as the human body—and can dramatically diffract, reflect, and scatter around dielectric structures, creating a more dynamic inverse scattering problem than EIT/ECT, which can be more computationally demanding.
Although the scattering behaviors are different in the low-frequency/static and microwave regimes, both generate ill-posed scattering data that cannot be definitively inverted to resolve the spatial and electrical characteristics of the scattering dielectric structure. The data generated in both regimes can be cumbersome and time consuming to solve and may have multiple mathematically possible solutions or no solution at all.
Thus, two key problems have limited broad use of dielectric impedance tomography in three-dimensional, inhomogeneous, or complex high dielectric constant structures, such as the human body. The first is the significant mismatch between the dielectric characteristics of these structures and the surrounding air. The second is solving the inverse of multi-path or scattered electromagnetic waves through complex structures—a mathematically ill-posed problem.
The impedance mismatch between differing dielectric materials severely limits non-contact measurements because the majority of measuring electromagnetic waves will reflect or refract from the specimen of interest, and wavelengths that provide reasonable spatial resolution in air (typically GHz and above) are extremely dissipative in many high-dielectric-constant specimens. This limitation is currently addressed by either measuring impedances through direct contact with the specimen or performing measurements in a dielectric matching media. Such constraints are not practical in many situations where throughput and disruption are concerns, such as medical trauma, security, or manufacturing applications.
Even when spatially diverse data is obtained, solving the internal structure of inhomogeneous dielectrics can prove intractable when the probing electromagnetic waves are free to propagate, resonate, and interfere with each other. Although much literature has been devoted to studying this mathematical problem, significant computational resources may be required to develop even cursory solutions.
Several techniques have been proposed for tackling the inherent issues in dielectric impedance tomography. For example, several issued U.S. patents detail methods requiring a probe or array of probes to come into full contact with a patient or specimen. For example, see U.S. Pat. Nos. 9,042,957, 8,391,968, and 5,807,251.
Electrical impedance tomography methods that do not require specimen contact either require intermediate media or use very short wavelengths and high powers. Electrical impedance tomography methods that do not require specimen contact but require intermediate media are described, for example, in several issued U.S. patents including: U.S. Pat. Nos. 8,010,187, 4,135,131, 7,164,105, and 7,205,782. For example, electrical impedance tomography methods that do not require specimen contact but use very short wavelengths and high powers are described, for example, in several issued U.S. patents including: U.S. Pat. Nos. 8,933,837, 7,660,452, and 7,664,303.
Capacitance measurement techniques or electrical capacitance tomography can offer advantages over impedance methods using freely propagating fields by completing a circuit between capacitor electrodes applied to the specimen. For example, systems that inherently use lower frequencies by constraining their propagation to the capacitor circuit for capacitive tomographic techniques are described, for example, in several issued U.S. patents including: U.S. Pat. Nos. 9,110,115 and 8,762,084. Although these techniques can reduce multi path complexity and attenuation of high frequencies, they require direct specimen contact and perform poorly in large or complex structures because electric fields are drawn to regions of a highest dielectric constant, looping around low dielectric constant regions or inhomogeneities, and potentially obscuring features of interest.
Where the dielectric profile to be studied extends only along a single dimension, transmission line methods have been successfully used. For example, in U.S. Pat. Nos. 9,074,922, and 4,240,445. See also, non-patent literature: Open-wire Transmission Lines Applied to the Measurement of the Macroscopic Electrical Properties of a Forest region, John Taylor, et al, Stanford Research Institute, October 1971; Coaxial Line Reflection Methods for Measuring Dielectric Properties of Biological Substances at Radio and Microwave Frequencies-A Review, IEEE Transactions on Instrumentation and Measurement (Volume: 29, Issue: 3, September 1980); and Electromagnetic Level Indicating (EMLI) System Using Time Domain Reflectometry, William J. Harney, Christopher P. Nemarich, Oceans '83, Proceedings, 29 Aug.-1 Sep. 1983.
There exists a need, therefore, for new systems and methods for tomographing dielectric materials that generate spatially solvable data and do not require excessively high frequencies, intermediate media, or intimate contact with the specimen under test.
Electromagnetic fields with linear or hard field characteristics would address these problems because they would yield tomographic data from a known and defined region. It is known that in a wave propagating in transverse electric (TE) or transverse electric and magnetic (TEM) modes, the electric fields are orthogonal to the direction of propagation. Therefore, if an electromagnetic field is propagating in a known direction and its propagation is determined to be in TE or TEM mode, linearity and direction of the electric fields can be assumed, creating a hard-field-like condition.
It is also known that in TE or TEM modes propagating through a media, propagation speed (Vprop) and impedance (Z) are related by the media's relative permittivity or dielectric constant (εr) as a component of its electric permittivity (ε=εr ε0), such that:
                                          Impedance            ⁡                          (              Z              )                                =                                    μ              ɛ                                      ⁢                                  ⁢                                  ⁢                              Speed            ⁡                          (                              V                prop                            )                                =                      1                                          ɛ                ⁢                                                                  ⁢                μ                                                    ⁢                                  ⁢                              V            prop                    =                      1                          ɛ              ⁢                                                          ⁢              Z                                                          (        1        )            
where μ is the material's magnetic permeability and ε0 is the permittivity of free space. The above relationship holds in TE transmission in an inhomogeneous dielectric comprised of structures that are sufficiently small relative to the probing wavelength (or whose traversal time comprises an insignificant fraction of the probing frequency's period), that the dielectric behaves as a mixture or composite dielectric with linear contributions from the constituent dielectrics as formulated by others as:
                              ɛ          eff                =                              ɛ            1                    ⁡                      (                                          ɛ                2                                                              ɛ                  2                                -                                                      f                    2                                    ⁡                                      (                                                                  ɛ                        2                                            -                                              ɛ                        1                                                              )                                                                        )                                              (        2        )            
where εeff is the effective dielectric constant of a mixture comprised of a first material with dielectric constant ε1 and a second material of dielectric constant ε2 comprising f2 volume fraction of the mixture.
However, in an inhomogeneous dielectric with larger structures, speed and impedance may be dominated by the E of certain constituent physical elements of the structure. For example, if the traversal time through constituent dielectric structures differs by more than a small fraction of the probing frequency's period, the geometries and orientation of the constituent dielectric structures must be taken into account and the above mix equation is no longer accurate. Analytic equations for complex structures of significant frequency fractions in traversal time or more are complex, not readily solved, and often do not have unique solutions.
A practical example of this phenomenon is a foamed polyethylene (PE) coaxial cable: a homogenous foamed PE dielectric creates a transmission line (such as an RG-59 cable) of 75 Ohms and propagation velocity (Vprop) of 83% the speed of light. Whereas the same structure containing the same volume of air and PE, but concentrated into regions of pure PE and pure air, will have regional characteristics of 60 Ohms and 66% Vprop for pure PE and 90 Ohms and 99% Vprop for air. If these bifurcated regions are aligned along the direction of propagation, the differing propagation velocities will disrupt TEM behavior and the wave will encounter significant dispersion between the slower and faster dielectric components. From a measurement perspective, the line's impedance (or composite εeff) and propagation velocity will be a complex function of the probing frequencies and the PE and air constituent geometries.
If, in the above example, the line could be restored to TE mode, the effective dielectric constant εeff can again become a linear function of the fraction of the constituent components such as Eq. 2 despite their bifurcation. This could be accomplished by inductively loading the center conductor of the coaxial cable to slow its velocity to match the slower solid PE constituent. An RG-63 coaxial cable is a practical manifestation of this behavior. By inductively loading the core conductor, RG-63 propagates in TEM mode with a uniform 125 ohms and 81% velocity despite containing a bifurcated PE and air dielectric along the direction of propagation.